• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.125-134
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• 1993

Let X be a compact Hausdorff space, and let C(X) (resp. $C_{R}$(X)) be the complex (resp. real) Banach algebra of all continuous complex-valued(resp. real-valued) functions on X with the pointwise operations and the supremum norm x. A Banach function algebra on X is a Banach algebra lying in C(X) which separates the points of X and contains the constants. A Banach function algebra on X equipped with the supremum norm is called a uniform algebra on X, that is, a uniformly closed subalgebra of C(X) which separates the points of X and contains the constants.s.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-182
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• 2011

The notions of bipolar fuzzy hyper MV-subalgebras, (weak) bipolar fuzzy hyper MV-deductive system and precisely weak bipolar fuzzy hyper MV-deductive system are introduced, and their relations are investigated. Characterizations of bipolar fuzzy hyper MV-subalgebras and weak bipolar fuzzy hyper MV-deductive systems are provided.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.317-331
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• 2018

This paper aims to extend the notion of hesitant fuzzy sets on UP-algebras to hesitant fuzzy soft sets over UP-algebras by merging the notions of hesitant fuzzy sets and soft sets. Further, we discuss the notions of hesitant fuzzy soft strongly UP-ideals, hesitant fuzzy soft UP-ideals, hesitant fuzzy soft UP-filters, and hesitant fuzzy soft UP-subalgebras of UP-algebras, and provide some properties.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.535-559
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• 2022

The notions of cubic intuitionistic fuzzy set to filters and implicative filters of BE-algebras are introduced. Relations between cubic intuitionistic fuzzy filters with cubic intuitionistic fuzzy implicative filters of BE-algebras are investigated. The homomorphic image and inverse image of cubic intuitionistic fuzzy filters are studied and some related properties are investigated. Also, the product of cubic intuitionistic fuzzy subalgebras (implicative filters) of BE-algebras are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.363-368
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• 2010

In this paper we construct a subalgebra $L_8$ of $M_8({\mathbb{R}})$ which is a generalization of the algebra of quaternions. Moreover we prove that the algebra $L_8$ is the real Clifford algebra $Cl_3$, and so $L_8$ is a matrix representation of Clifford algebra $Cl_3$.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.257-267
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• 2016

We find examples of Ideals in a tridiagonal algebra ALGL_∞ and study some properties of Ideals in ALGL_∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL_∞ and let A_2,{k} ⊂ A ⊂ {T ∈ ALGL_∞ | T_(2k-1,2k) = 0}. Then A is an ideal of ALGL_∞ if and only if A = A_2,{k} where A_2,{k} = {T ∈ ALGL_∞ | T_(2k-1,2k) = 0, T_(2k-1,2k-1) = T_(2k,2k) = 0}. Let B be a subalgebra of ALGL_∞ such that B_2,{j} ⊂ B ⊂ {T ∈ ALGL_∞ | T_(2j+1,2j) = 0}. Then B is an ideal of ALGL_∞ if and only if B = B_2,{j}, where B_2,{j} = {T ∈ ALGL_∞ | T_(2j+1,2j) = 0, T_(2j,2j) = T_(2j+1,2j+1) = 0}.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.657-673
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• 2009

The fixed point algebra $C^*(E)^{\gamma}$ of a gauge action $\gamma$ on a graph $C^*$-algebra $C^*(E)$ and its AF subalgebras $C^*(E)^{\gamma}_{\upsilon}$ associated to each vertex v do play an important role for the study of dynamical properties of $C^*(E)$. In this paper, we consider the stability of $C^*(E)^{\gamma}$ (an AF algebra is either stable or equipped with a (nonzero bounded) trace). It is known that $C^*(E)^{\gamma}$ is stably isomorphic to a graph $C^*$-algebra $C^*(E_{\mathbb{Z}}\;{\times}\;E)$ which we observe being stable. We first give an explicit isomorphism from $C^*(E)^{\gamma}$ to a full hereditary $C^*$-subalgebra of $C^*(E_{\mathbb{N}}\;{\times}\;E)({\subset}\;C^*(E_{\mathbb{Z}}\;{\times}\;E))$ and then show that $C^*(E_{\mathbb{N}}\;{\times}\;E)$ is stable whenever $C^*(E)^{\gamma}$ is so. Thus $C^*(E)^{\gamma}$ cannot be stable if $C^*(E_{\mathbb{N}}\;{\times}\;E)$ admits a trace. It is shown that this is the case if the vertex matrix of E has an eigenvector with an eigenvalue $\lambda$ > 1. The AF algebras $C^*(E)^{\gamma}_{\upsilon}$ are shown to be nonstable whenever E is irreducible. Several examples are discussed.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.61-69
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• 1991

By $C^{(1)}$[0, 1] we denote the Banach algebra of complex valued continuously differentiable functions on [0, 1] with norm given by $${\parallel}f{\parallel}=\sup_{x{\in}[0,1]}({\mid}f(x){\mid}+{\mid}f^{\prime}(x){\mid})\text{ for }f{\in}C^{(1)}$$. By A we denote the sub algebra of $C^{(1)}$ defined by $$A=\{f{\in}C^{(1)}:f(0)=f(1)\text{ and }f^{\prime}(0)=f^{\prime}(1)\}$$. By an isometry of A we mean a norm-preserving linear map of A onto itself. The purpose of this article is to describe the isometries of A. More precisely, we show tht any isometry of A is induced by a point map of the interval [0, 1] onto itself.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.37-43
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• 2014

In this paper, we show that for any ${\sigma}$-complete Boolean subalgebra $\mathcal{M}$ of $\mathcal{R}(X)$ containing $Z(X)^{\sharp}$, the Stone-space $S(\mathcal{M})$ of $\mathcal{M}$ is a basically diconnected cover of ${\beta}X$ and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed $\mathcal{M}$-ultrafilter} of the Stone-space $S(\mathcal{M})$ is the the minimal basically disconnected cover of X if and only if it is a basically disconnected space and $\mathcal{M}{\subseteq}\{\Lambda_X(A){\mid}A{\in}Z({\Lambda}X)^{\sharp}\}$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.367-373
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• 2007

For a unital *-subalgebra of the space $\mathcal{L}^a(X)$ of all adjointable maps on a Hilbert $\mathcal{B}$-module X with a $C^*$-algebra $\mathcal{B}$, we study unitary operator (in such algebra)-valued multiplier ${\sigma}$ on a normal, generating subsemigroup S of a group G with its extension to G. A dilation of a projective isometric ${\sigma}$-representation of S is established as a projective unitary ${\rho}$-representation of G for a suitable unitary operator (in some algebra)-valued multiplier ${\rho}$ associated with the multiplier ${\sigma}$ which is explicitly constructed.